Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking

Abstract

Interacting many-body systems that are driven far away from equilibrium can exhibit phase transitions between dynamically emerging quantum phases, which manifest as singularities in the Loschmidt echo. Whether and under which conditions such dynamical transitions occur in higher-dimensional systems with spontaneously broken continuous symmetries is largely elusive thus far. Here, we study the dynamics of the Loschmidt echo in the three dimensional O(N) model following a quantum quench from a symmetry breaking initial state. The O(N) model exhibits a dynamical transition in the asymptotic steady state, separating two phases with a finite and vanishing order parameter, that is associated with the broken symmetry. We analytically calculate the rate function of the Loschmidt echo and find that it exhibits periodic kink singularities when this dynamical steady-state transition is crossed. The singularities arise exactly at the zero-crossings of the oscillating order parameter. As a consequence, the appearance of the kink singularities in the transient dynamics is directly linked to a dynamical transition in the order parameter. Furthermore, we argue, that our results for dynamical quantum phase transitions in the O(N) model are general and apply to generic systems with continuous symmetry breaking.

7 pages, 6 figures

References in corpus (9)

• Fluctuation theorems: Work is not an observable
• Experimental Observation of a Generalized Gibbs Ensemble
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• First order dynamical phase transitions
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Exploring dynamical phase transitions and prethermalization with quantum noise of excitations
• Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits
• Dynamical Transition in Interaction Quenches of the One-Dimensional Hubbard Model

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